It’s not really a word

Since it’s used to convey meaning using letters and people understand that meaning, it by any definition that matters IS a word.

Also it clearly implies something is inherent to “Caucasians”

No. “Particularly Caucasians” ≠ “all Caucasians”.

I can’t be bothered to do any clever wordplay on the other supposed racial categories

Good, because that would likely be punching down, unlike pointing out how audacious some white people are with their privilege.

but I suspect any equivalent puns might be considered a little problematic, what what?

No, they wouldn’t be equivalent. Pointing out white privilege and criticizing those that wield it as both a sword and a shield is not the same as making fun of less privileged people or even white people who are aware of and don’t exploit their privilege.